assignment 2: problem 7 (1 point)\nlet f be the function whose graph is shown below.\nevaluate each of the…

assignment 2: problem 7 (1 point)\nlet f be the function whose graph is shown below.\nevaluate each of the following expressions.\n(if a limit does not exist or is undefined, enter \dne\.)\n1. $lim_{x\rightarrow - 1^{-}}f(x)=$\n2. $lim_{x\rightarrow - 1^{+}}f(x)=$\n3. $lim_{x\rightarrow - 1}f(x)=$\n4. $f(-1)=$\n5. $lim_{x\rightarrow 1^{-}}f(x)=$\n6. $lim_{x\rightarrow 1^{+}}f(x)=$\n7. $lim_{x\rightarrow 1}f(x)=$\n8. $lim_{x\rightarrow 3}f(x)=$\n9. $f(3)=$\nthe graph of $y = f(x)$.

assignment 2: problem 7 (1 point)\nlet f be the function whose graph is shown below.\nevaluate each of the following expressions.\n(if a limit does not exist or is undefined, enter \dne\.)\n1. $lim_{x\rightarrow - 1^{-}}f(x)=$\n2. $lim_{x\rightarrow - 1^{+}}f(x)=$\n3. $lim_{x\rightarrow - 1}f(x)=$\n4. $f(-1)=$\n5. $lim_{x\rightarrow 1^{-}}f(x)=$\n6. $lim_{x\rightarrow 1^{+}}f(x)=$\n7. $lim_{x\rightarrow 1}f(x)=$\n8. $lim_{x\rightarrow 3}f(x)=$\n9. $f(3)=$\nthe graph of $y = f(x)$.

Answer

Explanation:

Step1: Analyze left - hand limit at $x=-1$

As $x\to - 1^{-}$, follow the graph from the left, $y = 3$.

Step2: Analyze right - hand limit at $x=-1$

As $x\to - 1^{+}$, follow the graph from the right, $y=-3$.

Step3: Analyze limit at $x = - 1$

Since left - hand and right - hand limits are different, $\lim_{x\to - 1}F(x)$ DNE.

Step4: Find $F(-1)$

There is a closed - dot at $(-1,3)$, so $F(-1)=3$.

Step5: Analyze left - hand limit at $x = 1$

As $x\to1^{-}$, $y = 1$.

Step6: Analyze right - hand limit at $x = 1$

As $x\to1^{+}$, $y = 1$.

Step7: Analyze limit at $x = 1$

Since left - hand and right - hand limits are equal, $\lim_{x\to1}F(x)=1$.

Step8: Analyze limit at $x = 3$

As $x\to3$, $y=-1$.

Step9: Find $F(3)$

There is an open - dot at $x = 3$, so $F(3)$ DNE.

Answer:

  1. $3$
  2. $-3$
  3. DNE
  4. $3$
  5. $1$
  6. $1$
  7. $1$
  8. $-1$
  9. DNE